Appendix II.
891
p. 764, whose relation to the dry curve has been found, and plot
it, point for point, so that it bears the same relation to /V. The
transformation from p v to r <f> ordinates is next made : thus R and
s are projected vertically to T, and horizontally to u and v
respectively, on the proper constant-temperature line, and lastly u
and v are projected vertically to w and x, giving points on the r<f>
diagram.
Note that a constant volume line a b on the/ v diagram, when
projected rightward and upward at various temperatures, becomes
the curve b^ al on the r $ diagram; and the adiabatic de on the
T 0 diagram can be similarly projected back to the p v diagram.
Constant pressure lines are always parallel to base lines.
Finally, before leaving this important heat diagram, a few-
further applications will be shewn. Fig. 848 is the Rankine cycle,
where heat supplied is shewn by thick lines and the work done by
shaded area; then, ideal efficiency is calculated by taking the
base line at absolute zero. If the dotted figure be a card plotted
out, its included area divided by the shaded area will be the
comparison-ratio. Fig. 849 shews steam used non-expansively
but without the usual losses. Dividing the black area by the
shaded portion will give the comparison-ratio. Fig. 850 is the
usual indicator card with incomplete expansion, but without
cylinder condensation. Fig. 851 is a good indicator card with
sharp corners, and the decrease of work done is easily seen; due
to wetness from B to c, drop at release from c to D, compression
at EF, and clearance at EA. As BH is an adiabatic, the area
B G K H is additional liquefaction loss after cut-off, H j c L the gain
by re-evaporation, and H B M N the loss before cut-off. Fig. 852 is
for steam superheated before entering the cylinder, where <j> is
the entropy of the saturated steam, and fa that of the superheated
steam, the addition fa - <f> being found from the formula
•48 (loge^-loger)
There is nothing to be got by considering superheating by
pure theory. The only way is to compare the indicated heat,
shewn by black lines, of an actual engine, with the shaded area,
when the direction of saving is shewn, being a decrease of the
missing quantity when superheating.
3N